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To solve the equation \( x^2 = 39 \) where \( x \) is a real number, we need to take the square root of both sides:

\[
x = \pm \sqrt{39}
\]

Since \( x^2 = 39 \) implies that \( x \) could be either the positive or negative square root of 39, the simplified solution is:

\[
x = \pm \sqrt{39}
\]

We can approximate \( \sqrt{39} \) to make it more concrete:

\[
\sqrt{39} \approx 6.244
\]

So the approximate solution is:

\[
x \approx \pm 6.244
\]

Would you like a more detailed explanation or help with any related concepts? Here are some related questions you might explore:

1. What is the exact value of \( \sqrt{39} \) without approximation?
2. How do we know there are two solutions for \( x^2 = 39 \)?
3. How would we solve a similar equation with a different number on the right-hand side?
4. Can we simplify the square root of 39 further?
5. How do we check the solution by substituting back into the original equation?

**Tip:** Always remember to check for both the positive and negative square roots when solving equations of the form \( x^2 = k \), where \( k \) is positive.

Solve x^2 = 39, where x is a real number. Simplify your answer as much as possible.

Learn how to solve the quadratic equation x^2 = 39 by taking the square root of both sides. This problem explores key algebraic concepts, including square roots and real numbers. Suitable for students in Grades 8-10.

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